A 3D vector field representing the numerical results of a large-eddy simulation of Navier-Stokes equations for the MAX experiment [1]} is representative of turbulent mixing and thermal striping that occur in the upper plenum of liquid sodium fast reactors. The data, generated by the Nek5000 solver [2]}, have been resampled from their original topology onto a \(200 \times 200 \times 200\)  regular grid, and the magnitude of the velocity vector is associated with each 3D domain point [3]}.
Out of this dataset, a 2D slice (with \(\left| \Omega \right|=200\times 200\) ) along the midplane in axial direction is used for our first study here. The reference solution and the converged, reconstructed solution with \(\mathcal {N}=5 \times 5=25\)  subdomains with \(p=6\)  and \(\left| \delta \right|=2p\)  is shown in Fig. (REF ) for different compression ratios. Depending on the usecase for MFA reconstruction, the converged error norms with 20 floating control points per subdomain yielding a net compression of 4X is sufficient to evaluate continuous derivatives everywhere in the domain \(\Omega \) . A full MFA representation (with compression ratio=1) is also shown in Fig. (REF ), which can fully reconstruct the original features in the input dataset in contrast to Fig. (REF ) that shows a lossy smoothing of the sharp features in the original data.
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